Stardate 41263.1 A Starfleet Officer thinks he can improve the Enterprise's engines. However, it is his mysterious alien assistant that really holds the key to the miraculous distances the Enterprise is able to achieve. Then It becomes up to Wesley Crusher to get the starship back to their own galaxy, after the alien, now known as the "Traveler," falls ill.

Recap

Log Entries:
*Captain's Log, Stardate 41263.1. We have rendezvoused with the U.S.S. Fearless from which a Starfleet propulsion expert and his assistant are beaming over to conduct tests on the Enterprise's warp drive engines.
*Captain's Log, Stardate 41263.2. This will be a rather unusual log entry assuming Starfleet ever receives it. As I've already informed my crew a phenomenal surge of power during a warp speed experiment has sent our starship hurtling out of our own galaxy and past another taking us over 2,700,000 light years in a few minutes.
*Captain's Log, Stardate 41263.3. Instead of returning to our own galaxy the Enterprise has gone forward to a place in the universe which is uncharted and unknown. Our present position puts us at over a billion light years from our galaxy.
*Captain's Log, supplemental. Our position is unknown and our only chance of returning to the known universe is a dying alien who is generally humanoid but with a physiology sufficiently different from our own to create medical problems in caring for him.
*Captain's Log: Any time entry is meaningless. We have no choice but to repeat the same warp experiment but with one variation. A principal part of this warp formula will be the thoughts of everyone aboard the Enterprise. We have no idea exactly how this works. We understand only that the Traveler makes use of this somehow. It will be most important that those aboard avoid random thoughts that might change the reality of what we're attempting to do.
*Captain's Log, Stardate 41263.4. For outstanding performance in the best Starfleet tradition Wesley Crusher is made acting ensign with the duties and privileges of that rank and whether that rank becomes permanent, Mr Crusher depends on you.

We learn in this episode that Wesley has staggering abilities that the Traveler can see, but no one else but Picard must know about.